Abstract

In the paper, we introduce the concept of a preorder on a category and study its relation to categorical closure operators. In particular, employing a Galois connection, we show that there is a one-to-one correspondence between the idempotent closure operators and certain preorders on a category.

中文翻译：

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类别等幂闭包算子的阶数实现

摘要

在本文中，我们介绍了类别上的预购概念，并研究了其与分类闭包运算符的关系。特别是，通过使用Galois连接，我们证明了幂等闭包运算符与类别上的某些预序之间存在一一对应的关系。